Methods and systems for isochoric measurements using differential scanning calorimetry

ABSTRACT

In an embodiment is provided a method for measuring a vapor-liquid transition of a substance, the method including introducing a substance into a sample cell of a calorimetric block of a differential scanning calorimeter (DSC) at a first initial pressure, the system volume being constant; maintaining the substance in a vapor phase; cooling the substance at a cooling rate; and generating a thermogram. In another embodiment is provided a method for measuring a vapor-liquid transition of a substance, the method including introducing a substance into a sample cell of a calorimetric block of a DSC at a first initial pressure, the system volume being constant; maintaining the substance in a liquid phase; heating the substance at a heating rate; and generating a thermogram. In another embodiment is provided a method for measuring a vapor-liquid transition of a substance in the presence of an adsorbent.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/548,898, filed Aug. 23, 2019 (now U.S. Pat. No. 11,499,928), whichclaims priority to U.S. Provisional Patent Application No. 62/722,476,filed Aug. 24, 2018, each of which are hereby incorporated by referencein their entirety.

BACKGROUND Field

The present disclosure relates generally to methods and systems fordifferential scanning calorimetry (DSC), and more specifically toisochoric methods and systems for determining the onset conditions ofvapor-liquid phase transitions of pure components and mixtures in bulkand in nanopores.

Description of Related Art

Conventional thermal analyses commonly used to measure phase transitionsof substances and to identify, e.g., vapor pressures, are DifferentialThermal Analysis (DTA) and Differential Scanning calorimetry (DSC). Inboth methods, a test sample and a reference sample are heated and cooledunder identical conditions. In DTA, a temperature difference between thetest and reference samples is recorded and plotted against time ortemperature. When a thermal event, e.g., phase transition incrystallization occurs in the test sample, heat is released and thetemperature of the test sample rises above that of the reference sample,resulting in an exothermic peak. Similarly, when melting occurs in thetest sample, heat is absorbed and the temperature of the test sampledrops below that of the reference sample, resulting in an endothermicpeak. In heat-flux DSC, the heat flux (or flow) produced between thetest and reference samples due to the temperature difference between thesamples is calculated and recorded. The heating or cooling process iscontrolled by a single furnace. In power-compensation DSC, thetemperatures of the test sample and reference sample are substantiallyidentical and controlled by two separate furnaces. The power (or heatflow) utilized to maintain the test sample at a set temperature againstthe reference furnace is measured.

ASTM E1782 (Standard Test Method for Determining Vapor Pressure byThermal Analysis), revised in 2014, provides the conventional procedurefor vapor pressure measurement using DTA and DSC. For DSC, the standardtest method recommends placing the substance to be measured in ahermetically sealable pan with a single pinhole in the center of thelid. Pinhole sizes ranging from approximately 50 μm to 350 μm arerecommended to retain boiling endotherm sharpness. The vapor pressuremeasurement based on ASTM E1782 is an isobaric heating process, thepressure of which is maintained by a regulated vacuum or inert (ornon-reactive) gas. Such measurements, however, suffer from inaccurateresults because of, e.g., the vaporization and escape of sample throughthe pinhole. Such vaporization and escape of the sample is exacerbatedby the inert or non-reactive gas used to maintain the pressure of thesample cell. Proper selection of a gas in accordance with ASTM E1782 isa further obstacle in its widespread applicability because the inert gascan dissolve into the substance being measured and affect the phasetransition of the substance. In addition, conventional DSC methodscannot be used for volatile substances or high pressure systems becauseof, e.g., the pinhole in the sample cell and the dissolution of theinert gas.

Conventional DSC measurements additionally involve the difficult task ofdetermining several measurement parameters, e.g., the size of the testsample and the size of the pinhole, both of which are optimized with thescanning rate. In addition, dew points of substances are very difficultto determine with precision and accuracy, and conventional DSC thermalanalyses, including the DSC isobaric method standardized in ASTM E1782,are typically incapable of measuring dew points. Instead, dew-pointmeasurements are typically derived by detecting the presence ofcondensate (visual determination), the change in fluid properties, orthe change in slope of the curve of measured properties, such as densityor volume versus pressure or temperature, upon crossing the substance'sphase boundary.

For DTA, the standard test method is an isobaric process performed atatmospheric pressure or at an applied pressure of an inert ornon-reactive gas, and recommends the use of capillary tubes, such asthose having an inside diameter of 2-4 mm and a length of 25 mm. Thesecapillary tubes can minimize, but not prevent, the escape of vapors, andthus DTA-based approaches are also inaccurate for determining the onsetconditions of phase transitions of pure substances and mixtures ofsubstances.

Measuring phase transitions of confined substances represent anotherchallenge to conventional thermal analytical methods. Confinement inpores (e.g., nanopores) can affect a substance's fluid phase behaviorby, for example, lowering the substance's vapor-to-liquid phasetransition curve. Understanding the phase behavior of confinedsubstances finds important applications in catalysis, carbon dioxidesequestration, drug delivery, enhanced coalbed methane recovery,pollution control, and separation, as well as hydrocarbon productionfrom shale and other tight formations. Conventional methods forinvestigating the phase behavior of a confined pure compound generallyutilize adsorption-desorption methods using different porous media. Suchmethods, however, are time consuming and costly, and often utilizeexpensive instrumentation. For example, the measurement of a singlecapillary condensation point can take days or even weeks. In addition,these adsorption-desorption methods suffer from inaccurate resultsbecause of, e.g., using the inflection point of an isotherm to determinethe capillary condensation point. Moreover, experiments on fluidmixtures in a confined space are performed less often due to their morecomplex nature. Consequently, features such as the dew points andcritical points of confined fluid mixtures suffer from minimal ornon-existent experimental exploration, thus rendering a fundamentalunderstanding of such systems far from complete.

Therefore, there is a need for improved methods of measuring vaporpressures of pure components and dew points of mixtures in bulk and inpores (e.g., nanopores) that overcome the problems of conventionalmeasurements such as inaccurate results and cost inefficiency. Moreover,the ability to accurately measure volatile substances, high pressuresystems, capillary condensation, and capillary evaporation of purecomponents and mixtures remains a need.

SUMMARY

In an embodiment is provided a process for measuring a vapor-liquidtransition of a substance in a constant volume system, the processincluding (a) introducing a substance into a sample cell of acalorimetric block of a differential scanning calorimeter (DSC) at afirst initial pressure, the system volume being constant; (b)maintaining the substance in a vapor phase; (c) cooling the substance ata cooling rate; and (d) generating a thermogram.

In another embodiment is provided a process for measuring a vapor-liquidtransition of a substance in a constant volume system, the processincluding (a) introducing a substance into a sample cell of acalorimetric block of a differential scanning calorimeter (DSC) at afirst initial pressure, the system volume being constant; (b)maintaining the substance in a liquid phase; (c) heating the substanceat a heating rate; and (d) generating a thermogram.

In another embodiment is provided a process for measuring a vapor-liquidtransition of a substance in a constant volume system, the processincluding (a) introducing an adsorbent into a sample cell of acalorimetric block of a differential scanning calorimeter, the systemvolume being constant; (b) introducing a substance into the sample cellat a first initial pressure; (c) maintaining the substance in a vaporphase or maintaining the substance in a liquid phase; (d) cooling thesubstance at a cooling rate when the process comprises maintaining thesubstance in a vapor phase, or heating the substance at a heating ratewhen the process comprises maintaining the substance in a liquid phase;and (e) generating a thermogram.

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above-recited features of the presentdisclosure can be understood in detail, a more particular description ofthe disclosure, briefly summarized above, may be had by reference toembodiments, some of which are illustrated in the appended drawings. Itis to be noted, however, that the appended drawings illustrate onlytypical embodiments of this disclosure and are therefore not to beconsidered limiting of its scope, for the disclosure may admit to otherequally effective embodiments.

FIG. 1A is a typical pressure-temperature diagram with isochores of apure substance.

FIG. 1B is a typical pressure-temperature diagram with isochores of amixture of substances.

FIG. 2A is an example thermogram and pressure history of a CO₂ vaporpressure measurement according to at least one embodiment of the presentdisclosure.

FIG. 2B shows example vapor pressure measurements of CO₂ and acomparative vapor pressure measurement of CO₂ according to at least oneembodiment of the present disclosure.

FIG. 3 shows an example continuous measurement of the vapor pressure ofCO₂ relative to comparative data according to at least one embodiment ofthe present disclosure.

FIG. 4A is an example thermogram and pressure history of a dew pointmeasurement of a methane/ethane gas mixture according to at least oneembodiment of the present disclosure.

FIG. 4B shows example dew point measurements of a methane/ethane gasmixture and a comparative dew point measurements of a methane/ethane gasmixture according to at least one embodiment of the present disclosure.

FIG. 5A is an example thermogram and pressure history for the capillarycondensation of CO₂ in SBA-15 and the bulk condensation of CO₂ accordingto at least one embodiment of the present disclosure.

FIG. 5B shows example and comparative capillary condensationmeasurements and bulk condensation measurements of CO₂ according to atleast one embodiment of the present disclosure.

FIG. 5C shows example and comparative capillary condensationmeasurements and bulk condensation measurements of CO₂ according to atleast one embodiment of the present disclosure.

FIG. 6A is an example thermogram and pressure history for the capillarycondensation of a methane/ethane gas mixture in SBA-15 and the bulkcondensation of the methane/ethane gas mixture according to at least oneembodiment of the present disclosure.

FIG. 6B shows example and comparative capillary condensationmeasurements and bulk condensation measurements of a methane/ethane gasmixture in SBA-15 according to at least one embodiment of the presentdisclosure.

FIG. 6C shows example and comparative capillary condensationmeasurements and bulk condensation measurements of a methane/ethane gasmixture according to at least one embodiment of the present disclosure.

FIG. 7A is an example thermogram and pressure history of a CO₂ vaporpressure measurement according to at least one embodiment of the presentdisclosure.

FIG. 7B shows example evaporation point measurements of CO₂ and ethane acomparative measurements of CO₂ and ethane according to at least oneembodiment of the present disclosure.

FIG. 8A shows an example thermogram of a continuous measurement of thevapor pressure of CO₂ relative according to at least one embodiment ofthe present disclosure.

FIG. 8B shows an example continuous measurement of the vapor pressure ofCO₂ and ethane relative to comparative data according to at least oneembodiment of the present disclosure.

FIG. 9A is an example thermogram and pressure history for the capillaryevaporation of CO₂ in SBA-15 according to at least one embodiment of thepresent disclosure.

FIG. 9B shows example capillary evaporation measurements and bulkevaporation measurements of CO₂ in SBA-15 (adsorbent S2) according to atleast one embodiment of the present disclosure.

FIG. 9C shows example capillary evaporation measurements and bulkevaporation measurements of ethane in SBA-15 (adsorbent S2) according toat least one embodiment of the present disclosure.

FIG. 9D shows example capillary evaporation measurements and bulkevaporation measurements of CO₂ in SBA-15 (adsorbent S3) according to atleast one embodiment of the present disclosure.

FIG. 9E shows example capillary evaporation measurements and bulkevaporation measurements of ethane in SBA-15 (adsorbent S3) according toat least one embodiment of the present disclosure.

FIG. 10 shows an example apparatus used to determine the vapor-liquidphase transitions according to at least one embodiment of the presentdisclosure.

DETAILED DESCRIPTION

The present disclosure provides isochoric methods and systems formeasuring vapor pressures of pure substances and the dew points of abulk mixture in the absence of pores (e.g., micropores and nanopores).The present disclosure also provides isochoric methods and systems formeasuring vapor pressures of pure substances and the dew points of abulk mixture in the presence of pores.

Isobaric DSC has been widely used to measure solid transition(melting/crystallization), and thus solid-liquid equilibria andsolid-liquid-vapor equilibria, of many pure compounds and multicomponentmixtures. However, the measurement of condensation/evaporation, e.g.,vapor-liquid equilibrium, using thermal analyses can be more difficult.DTA instruments that employ capillary tubes and isobaric DSCmeasurements including the methods of ASTM E1782 cannot accuratelymeasure vapor pressures of pure substances and bubble points/dew pointsof mixtures of substances. Determination of dew points is desirable, forinstance, when dealing with mixtures that exhibit retrogradecondensation, such as natural gases.

The inventors have discovered an isochoric method that accuratelydetermines the onset conditions for vapor-liquid phase transitions forsubstances and mixtures of substances in bulk and in pores, e.g.,nanopores. The onset conditions include vapor pressures of pure, orsubstantially pure, substances and dew points of mixtures including twoor more substances. The isochoric methods and systems described hereinrival and/or surpass conventional methods for measuring vapor pressures,dew points, capillary condensation, and capillary evaporation ofsubstances. Conventional methods, such as isobaric DSC, requireoptimization of the sample size, the pinhole size of the sample cell,and the heating rate of the sample in order to achieve accurate results.In contrast, the methods provided herein are not constrained byconventional limitations, because there are no sample size and pinholesize to optimize. Moreover, in contrast to conventional methods wherethe scanning rate (e.g., heating/cooling rate) of the sample is sampledependent, the same or similar scanning rates can be used acrosssubstances for the isochoric systems and methods described herein.

Moreover, the methods and systems described herein are applicable to, atleast, volatile substances, high pressure systems, and dew point (orcapillary condensation, capillary evaporation) measurements. Theconventional isobaric process, e.g., the ASTM method, is intended forbubble-point measurements and not for dew point measurements. Volatilesubstances may evaporate and escape through the pinhole of the samplepan when performing conventional DSC methods. Similarly high pressuresystems cannot be studied by conventional methods due to, e.g., thedissolution of inert gas. In contrast, the methods described herein donot utilize a sample pan having a pinhole. Conventional DSC measurementsutilize an inert or non-reactive gas to control the pressure of thesample cell, but at certain pressures (e.g., high pressures), the gascan dissolve into the substance being measured and will affect the phasetransition. In at least that sense, the gas may no longer be consideredinert as it affects at least the bubble point of the substance beingmeasured. The methods described herein do not utilize an inert ornon-reactive gas being introduced to the sample cell.

Conventional techniques to characterize confined substances, such asadsorption experiments, using open-flow apparatus at constant pressuresand gravimetric adsorption-desorption experiments for capillarycondensation and capillary evaporation measurements of substances innanopores have been performed. However, these conventional techniquessuffer from high costs, are very time consuming, and are inaccurate.Light scattering, nuclear magnetic resonance, and positron annihilationspectroscopy, under isobaric conditions, have also been performed tomeasure capillary condensation and capillary evaporation of substancesand mixtures. These conventional techniques can only be used for lowpressure measurements. Moreover, the light scattering technique isrestricted to use of a clear glass rod for the adsorbent.

More recently an isobaric procedure using DSC, i.e., an extension ofASTM E1782, was used to study the phase behavior of hydrocarbon mixturesin nanopores. However, this isobaric DSC procedure provides inaccurateresults because the vaporization and escape of sample through thepinhole changed the mixture composition before reaching the bubble pointof the fluids in the pore. As described above, the isobaric DSC methodwill not work for confined mixtures that contain volatile components andit would be difficult, if not impossible, to accurately measure thephase transition of mixtures at high pressures due to the dissolution ofthe inert or non-reactive gas used. Furthermore, the isobaric DSC methodalso suffers from difficulties in determining several measurementparameters, e.g., the size of the test sample, the size of the pinhole,and the scanning rate.

In addition, adsorption experiments can be very time consuming. Forexample, measuring one capillary condensation point or capillaryevaporation point by a typical adsorption experiment can take days, oreven weeks. In contrast, the isochoric DSC methods described herein canmeasure a capillary condensation point/capillary evaporation point in afew hours. Therefore, the DSC methods described herein can have lowerlabor and operation costs than typical methods for measuring confinedfluids. Moreover, conventional adsorption experiments provide inaccurateresults because the capillary condensation point/capillary evaporationpoint is determined from the inflection point of an isotherm. Such adetermination is inaccurate because to find the inflection point, thedata is fitted to a mathematical function or is numericallydifferentiated to find the maximum slope (rate of change). If the dataobtained in constructing an isotherm are scattered, e.g., have largeexperimental error, or do not show a clear maximum slope, which ispretty common in such experiments, it is difficult to find a propermathematical function or to find the maximum slope, and thus thedetermination of the inflection point becomes inaccurate.

Moreover, experiments on fluid mixtures in a confined space areperformed less often due to their more complex nature. Even for fluidsin the bulk phase, the phase behavior of mixtures are more complex thanthat of pure substances. While there is only one vapor pressure curve(or vapor-liquid transition curve) for pure substances, there are twodifferent vapor-liquid transition curves for mixtures, e.g., dew-pointand bubble-point curves. In the critical region, e.g., the region closeto the critical point, of mixtures, the gas mixture can be condensed bydecreasing or increasing the pressure depending on the mixture ofinterest and the initial pressure. For pure substances, the gas mixturecan be condensed only by increasing the pressure. Consequently, featuressuch as the dew points and critical points of confined fluid mixturessuffer from minimal or non-existent experimental exploration, thusrendering a fundamental understanding of such systems far from complete.

The methods described herein overcome these problems because thecapillary condensation point/capillary evaporation point is determinedfrom the peak of the thermogram. Using the peak of the thermogram ismore accurate because the peak of the thermogram is very clear andcorresponds directly to the phase transition. In addition, the typicalinstrumentation utilized for measuring confined fluids, such as anadsorber or other custom-built devices for adsorption-desorptionexperiments, are expensive or even cost prohibitive for certainindustries and/or applications. In contrast, DSC instrumentation can bemuch less expensive, and thereby permitting more widespread use.

The present disclosure includes an isochoric method for measuring theonset of vapor-liquid phase transition of pure components and mixturesin bulk and nanopores. The method can be performed with the use of aDSC, such as a high-pressure micro differential scanning calorimeter.The method can be used to measure vapor pressures and dew points ofvarious pure (or substantially pure) liquids and gases, and mixturesthereof, in bulk and in nanopores at different pressures ortemperatures. As explained above, the method can be used to measure theonset of vapor-liquid phase transition for substances and mixtures ofsubstances that isobaric methods cannot measure and eliminates manydifficulties encountered in isobaric methods.

FIG. 1A shows a generic pressure-temperature (P-T) diagram withisochores for a pure component. When the starting point is point A inthe gas phase and the cooling process is performed for a closed systemat constant volume (e.g., the test system has a fixed volume), the P-Tpath of the DSC cooling process proceeds along the isochore until itreaches the saturated vapor pressure curve at point B. This is the dewpoint where the first drop of liquid appears.

FIG. 1B shows a generic P-T diagram with isochores for a mixture at acertain composition. As in the case of pure component, the idealisochoric dew and bubble point measurements will follow the isochore, inwhich the conditions for the first drop of liquid and the first bubbleof vapor, respectively, can be determined on cooling. In mixtures, thedew points and bubble points lie on different curves on the phasediagram sandwiching the two-phase immiscibility region.

Isochoric Dew-Point Measurement Methods

In at least one embodiment, a method for measuring a vapor-liquidtransition of a substance in a constant volume system can include (a)introducing a substance into a sample cell of a calorimetric block of adifferential scanning calorimeter (DSC) at a first initial pressure, thesystem volume being constant; (b) maintaining the substance in a vaporphase; (c) cooling the substance in the constant volume system at acooling rate; and (d) generating a thermogram. The thermogram output canbe used to determine the conditions, e.g., the pressure and temperature,of the substance's phase transition.

In some embodiments, the isochoric dew-point measurement method furtherincludes repeating operations (a)-(d) at different initial pressures inoperation (a), such as at least two, at least four, or at least fiveinitial pressures. The different initial pressures can be higher orlower than the first initial pressure. The method can be repeated atdifferent initial pressures in order to measure different conditions,e.g., pressure and temperature, of the substance's phase transition.

Initial pressures useful for the isochoric dew-point measurement methodcan depend on the substance being investigated. For CO₂, the initialpressures can be from about 5 bar to about 75 bar, such as about 10 bar,about 25 bar, about 40 bar, about 55 bar, or about 70 bar. For ethane,the initial pressures can be from about 1 bar to about 50 bar, such asabout 15 bar, about 20 bar, about 25 bar, about 30 bar, or about 35 bar.For a methane/ethane gas mixture, the initial pressures can be fromabout 5 bar to about 55 bar, such as about 10 bar, about 20 bar, about30 bar, about 40 bar, or about 50 bar.

In at least one embodiment, an adsorbent can be introduced into thesample cell of the calorimetric block of the DSC. For example, themethod can include introducing an adsorbent into the sample cell of thecalorimetric block of a differential scanning calorimeter, the samplecell being a constant volume system. This operation can be performedbefore introducing the substance into the sample cell at a first initialpressure. This operation can also be repeated for measurements atdifferent initial pressures. The adsorbent can be an adsorbent that hasmicropores, mesopores, nanopores, or a combination thereof. Examples ofmesoporous particles include those particles comprising silica,amorphous silica alumina, such as zeolites (e.g., ZSM and USY) andsilicoaluminophosphates. Other mesoporous particles can include SBA-15,MCM-41, and particles that exist in rock formations such as shale.

In some embodiments where an adsorbent is used with a pure substance,the amount of adsorbent can be varied. In at least one embodiment whenan adsorbent is used with a mixture, the amount of adsorbent can bevaried and the amount of adsorbent can be selected such that the amountdoes not change (or has a minor effect on) the composition of themixture in the bulk. The amount can vary depending on the mixture beingmeasured and the adsorbent.

In at least one embodiment, the isochoric dew-point measurement methodcan include evacuating the system (which includes the sample cell) priorto introducing the substance into the sample cell. The system includesthe calorimetric block of the differential scanning calorimeter (DSC).This operation can also be repeated for measurements at differentinitial pressures. In at least one embodiment, maintaining the substancein a vapor phase can include heating or cooling the sample, depending onthe phase of the sample being introduced. In at least one embodiment,maintaining the substance in a vapor phase can include heating orcooling the sample cell to an initial temperature above the saturationtemperature (e.g., the boiling point temperature) of the substance,heating or cooling the sample cell to an initial temperature above thedew point temperature of the substance, or a combination thereof.

Example substances to be measured by the methods provided herein andexample scanning rates used in the methods described herein are providedbelow.

Isochoric Evaporation-Point Methods

In at least one embodiment, a method for measuring a vapor-liquidtransition of a substance in a constant volume system can include (a)introducing a substance into a sample cell of a calorimetric block of adifferential scanning calorimeter (DSC) at a first initial pressure, thesystem volume being constant; (b) maintaining the substance in a liquidphase; (c) heating the substance in the constant volume system at aheating rate; and (d) generating a thermogram. The thermogram output canbe used to determine the conditions, e.g., the pressure and temperature,of the substance's phase transition.

In some embodiments, the isochoric evaporation-point measurement methodfurther includes repeating operations (a)-(d) at different initialpressures in operation (a), such as at least two, at least four, or atleast five initial pressures. The different initial pressures can behigher or lower than the first initial pressure. The procedure can berepeated at different initial pressures in order to measure differentconditions, e.g., pressure and temperature, of the substance's phasetransition. Initial pressures that can be used for the evaporation-pointmeasurement method include those provided above.

In some embodiments, the isochoric evaporation-point measurement methodcan be used with an adsorbent. Example adsorbents, and a discussionthereof, useful for the isochoric evaporation point method describedherein is provided above.

In at least one embodiment, the isochoric evaporation-point measurementmethod can include evacuating the system (which includes the samplecell) prior to introducing the substance into the sample. The systemincludes the calorimetric block of the differential scanning calorimeter(DSC). This method can also be repeated for measurements at differentinitial pressures. In at least one embodiment, maintaining the substancein a liquid phase can include heating or cooling the sample, dependingon the phase of the sample being introduced. In at least one embodiment,maintaining the substance in a liquid phase can include heating orcooling the sample cell to an initial temperature below the saturationtemperature (e.g., the boiling point temperature) of the substance,heating or cooling the sample cell to an initial temperature below theevaporation point temperature of the substance, or a combinationthereof.

The substance to be measured by the methods provided herein can be anysubstance capable of being measured by a DSC instrument. That is, aconstraint imposed on the type of substance can be based to thespecification of the DSC instrument. For example, a DSC can operatewithin a certain range of pressures and/or temperatures, which canprevent measurements on certain substances. A DSC that operates at verylow temperatures, such as −196° C., can allow for measurements on thevapor pressure and capillary condensation of methane.

Non-limiting examples of substances that can be measured by the methodsprovided herein include organic compounds and inorganic compounds, suchas hydrocarbons, substituted hydrocarbons, organic mixtures, and/oraqueous mixtures that contain salts. The hydrocarbons and substitutedhydrocarbons can be linear, branched, or cyclic (including polycyclic),and when cyclic, aromatic or non-aromatic ring structures.

Suitable hydrocarbons and substituted hydrocarbons can include C₁-C₁₀₀unsubstituted or C₁-C₁₀₀ substituted hydrocarbons (such as C₁-C₄₀unsubstituted or C₁-C₄₀ substituted hydrocarbons, such as C₁-C₂₀unsubstituted or C₁-C₂₀ substituted hydrocarbons, such as C₁-C₁₀unsubstituted or C₁-C₁₀ substituted hydrocarbons, such as C₁-C₆unsubstituted or C₁-C₆ substituted hydrocarbons) that may be linear,branched, or cyclic, and when cyclic, aromatic or non-aromatic. Examplesof such hydrocarbons include, but are not limited to, methane, ethane,n-propane, n-butane, isobutane, sec-butane, tert-butane, pentane,isopentane, hexane, octane, cyclopropane, cyclobutane, cyclopentane,cyclohexane, cyclooctane, aryl groups, such as benzene, toluene,naphthalene, and their substituted analogues.

The term “substituted hydrocarbon” refers to a hydrocarbon in which atleast one hydrogen atom of the hydrocarbon has been substituted with atleast one heteroatom (such as halogen, e.g., Br, Cl, F or I) orheteroatom-containing group (such as a functional group, e.g., —NR*₂,—OR*, —SR*, —SeR*, —TeR*, —PR*₂, —AsR*₂, —SbR*₂, —BR*₂, —SiR*₃, —GeR*₃,—SnR*₃, —PbR*₃, —(CH₂)_(q)—SiR*₃, and the like, where q is 1 to 10 andeach R* is independently hydrogen, a hydrocarbon, and two or more R* mayjoin together to form a substituted or unsubstituted completelysaturated, partially unsaturated, or aromatic cyclic or polycyclic ringstructure), or where at least one heteroatom has been inserted within ahydrocarbon ring. Cyclic structures (including aromatic structures) caninclude substituted and unsubstituted C₄-C₆₂ cyclic structures, such assubstituted and unsubstituted C₄-C₂₀ cyclic structures, such assubstituted and unsubstituted C₃-C₁₀ cyclic structures, and theirsubstituted analogs. Examples of such cyclic structures includecyclohexane, cyclopentane, and their substituted analogs.

Aromatic structures can include phenyl, naphthyl, xylyl, andheteroaromatic structures. Heteroaromatic structures include thosestructures where a ring carbon atom (or two or three ring carbon atoms)has been replaced with a heteroatom, such as N, O, or S. Aromaticstructures can also include pseudoaromatic heterocycles. The aromaticstructures can be substituted, whereby one or more hydrogen groups isreplaced by a hydrocarbon, substituted hydrocarbon, heteroatom, orheteroatom containing group. The heteroaromatic structures can besubstituted whereby one or more hydrogen groups is replaced by ahydrocarbon, substituted hydrocarbon, heteroatom, or heteroatomcontaining group.

Where isomers of a named hydrocarbon or aromatic structure exist (e.g.,n-pentane and iso-pentane) reference to one member of the group (e.g.,n-pentane) shall expressly disclose the remaining isomers (e.g.,iso-pentane) in the family. Likewise, reference to a hydrocarbon, asubstituted hydrocarbon, an aromatic structure, substituted aromaticstructure, heteroaromatic structure, and substituted heteroaromaticstructure without specifying a particular isomer (e.g., pentane)expressly discloses all isomers (e.g., n-pentane, iso-pentane).

Substituted hydrocarbons can include alcohols and ethers, such asmethanol, ethanol, propanol, isopropanol, n-butanol, isobutanol,tert-butanol, pentanol, hexanol, heptanol, octanol, decanol, phenol,ethylene oxide, diethyl ether, methoxyethane, dimethoxyethane,methoxybutane, tetrahydrofuran, glycols, anisole. The hydrocarbon groupof the alcohol and ether can be an alkyl group or an aryl group (such asa C₁-C₂₀, such as a C₁-C₁₀ hydrocarbon, such as a C₁-C₆ hydrocarbon).The alkyl group may be straight chain, branched, or cyclic. The alkylgroup may be saturated or unsaturated.

Further non-limiting examples of substances that can be measured by themethods provided herein include substances that are gases at about 25°C. and about 1 atm, such carbon containing gases, such as CO and CO₂, aswell as those substances discussed above that are gases at about 25° C.and about 1 atm such as methane. Other gases that can be measuredinclude N₂, SO₂, and Ar. Further non-limiting examples of substancesthat can be measured by the methods provided herein include substancesthat are liquids at about 25° C. and about 1 atm, such carbon containingliquids, such as those substances discussed above that are liquids atabout 25° C. and about 1 atm such as pentane. The substances can beextracted from shale, petroleum reservoirs, coalbeds, rock formations.In some embodiments, the substance is natural gas.

In some embodiments, the substance to be measured can be a puresubstance that is free from other components. The substance can besubstantially pure, such as about 95% pure, or 99% pure. The substanceto be measured can include binary mixtures, or mixtures comprising morethan two substances. The mixture can contain an unlimited number ofsubstances, though a constraint can be the ability to accurately measurethe amount of the individual substances in the mixture being tested.

The DSC scanning rate can influence the thermogram and the quality ofthe results obtained. The scanning rate can be referred tointerchangeably as the cooling rate or the heating rate. In the methodsprovided herein, if the scanning rate is low enough, the system can beassumed to be at equilibrium throughout the process, and the recordedpressures corresponding to the controlled temperatures represent theequilibrium pressures.

In some embodiments, the scanning rate (or heating rate or cooling rate)for the methods provided herein can be about 0.005° C./min or more, suchas from about 0.005° C./min to about 10° C./min or to about 5° C./min,such as from about 0.01° C./min to about 1° C./min, such as from about0.01° C./min to about 0.5° C./min, such as from about 0.01° C./min toabout 0.1° C./min, such as about 0.01° C./min, about 0.02° C./min, about0.03° C./min, about 0.04° C./min, about 0.05° C./min, about 0.06°C./min, about 0.07° C./min, such as about 0.08° C./min, about 0.09°C./min, or about 0.1° C./min. In some embodiments, the scanning rate forthe methods provided herein is about 10° C./min or less, such as about5° C./min or less, such as about 2° C./min or less, such as about 1°C./min or less, such as about 0.5° C./min or less, such as about 0.3°C./min or less, such as about 0.2° C./min or less, such as about 0.1°C./min or less, such as about 0.05° C./min or less, such as about 0.03°C./min or less, such as about 0.02° C./min or less, such as about 0.01°C./min or less.

Depending on whether the substance of interest is in the liquid phase orthe gas phase in the sample cell, the scanning rate can be a coolingrate or a heating rate. For example, when the substance of interest isin the gas phase in the sample cell (e.g., CO₂), the system temperatureis decreased at a constant cooling rate while the heat flow and pressurehistory are continuously recorded. When the substance of interest existsin the liquid phase in the sample cell (e.g., methanol), the systemtemperature is heated at a constant heating rate while the heat flow andpressure history are continuously recorded.

The scanning rate can be a cooling rate or a heating rate based onwhether the isochoric DSC measurement method is the isochoric dew-pointmeasurement method or isochoric evaporation-point measurement method.When the isochoric dew-point measurement method is used, the scanningrate can be a cooling rate. When the isochoric evaporation-pointmeasurement method is used, the scanning rate can be a heating rate.

Embodiments Listing

The present disclosure provides, among others, the followingembodiments, each of which may be considered as optionally including anyalternate embodiments.

Clause 1. A process for measuring a vapor-liquid transition of asubstance in a constant volume system, comprising: (a) introducing asubstance into a sample cell of a calorimetric block of a differentialscanning calorimeter (DSC) at a first initial pressure, the systemvolume being constant; (b) maintaining the substance in a vapor phase;(c) cooling the substance at a cooling rate; and (d) generating athermogram.

Clause 2. A process for measuring a vapor-liquid transition of asubstance in a constant volume system, comprising: (a) introducing asubstance into a sample cell of a calorimetric block of a differentialscanning calorimeter (DSC) at a first initial pressure, the systemvolume being constant; (b) maintaining the substance in a liquid phase;(c) heating the substance at a heating rate; and (d) generating athermogram.

Clause 3. The process of Clause 1 or Clause 2, further comprisingevacuating the system prior to introducing the substance into the samplecell.

Clause 4. The process of any one of Clauses 1 to 3, further comprising:performing operation (a) at a second initial pressure, the secondinitial pressure being different from the first initial pressure; andperforming operations (b), (c), and (d).

Clause 5. The process of any one of Clauses 1 to 4, further comprising:performing operations (a)-(d) at a series of initial pressures, theinitial pressures being different from each other and from the first andsecond initial pressures.

Clause 6. The process of any one of Clauses 1 to 5, wherein thesubstance is a pure substance.

Clause 7. The process of any one of Clauses 1 to 5, wherein thesubstance is a substantially pure substance.

Clause 8. The process of any one of Clauses 1 to 5, wherein thesubstance is more than one compound.

Clause 9. The process of any one of Clauses 1 to 5, wherein thesubstance is a gas at 25° C. and 1 atm.

Clause 10. The process of any one of Clauses 1 to 5, wherein thesubstance is a liquid at 25° C. and 1 atm.

Clause 11. The process of any one of Clauses 1 to 11, wherein when theprocess includes cooling the substance at a cooling rate, the coolingrate is from about 0.01° C./min to about 1° C./min, or from about 0.01°C./min to about 0.5° C./min, or from about 0.01° C./min to about 0.1°C./min; or wherein when the process includes heating the substance at aheating rate, the heating rate is from about 0.01° C./min to about 1°C./min, or from about 0.01° C./min to about 0.5° C./min, or from about0.01° C./min to about 0.1° C./min.

Clause 12. The process of any one of Clauses 1 to 11, wherein when theprocess includes cooling the substance at a cooling rate, the coolingrate is about 0.03° C./min; or wherein when the process includes heatingthe substance at a cooling rate, the heating rate is about 0.03° C./min.

Clause 13. The process of any one of Clauses 1 to 12, wherein thesubstance comprises a hydrocarbon (such as a C₁-C₂₀ unsubstitutedhydrocarbon, such as a C₁-C₁₀ unsubstituted hydrocarbon), a substitutedhydrocarbon (such as a C₁-C₂₀ substituted hydrocarbon, such as a C₁-C₁₀substituted hydrocarbon), or a combination thereof.

Clause 14. The process of any one of Clauses 1 to 13, wherein thesubstance comprises methane, ethane, methanol, or a combination thereof.

Clause 15. The process of any one of Clauses 1 to 10, wherein thesubstance comprises a gas such as Na, SO₂, Ar, a carbon containing gas(such as CO and/or CO₂), or a combination thereof.

Clause 16. The process of any one of Clauses 1 to 15, further comprisingdetermining the conditions (e.g., a pressure and a temperature) of thesubstance's phase transition based on the thermogram.

Clause 17. A process for measuring a vapor-liquid transition of asubstance in a constant volume system in the presence of adsorbent,comprising: (a) introducing an adsorbent into a sample cell of acalorimetric block of a differential scanning calorimeter, the systemvolume being constant; (b) introducing a substance into the sample cellat a first initial pressure; (c) maintaining the substance in a vaporphase; (d) cooling the substance at a cooling rate; and (e) generating athermogram.

Clause 18. A process for measuring a vapor-liquid transition of asubstance in a constant volume system, comprising: (a) introducing anadsorbent into a sample cell of a calorimetric block of a differentialscanning calorimeter, the system volume being constant; (b) introducinga substance into the sample cell at a first initial pressure; (c)maintaining the substance in a liquid phase; (d) heating the substanceat a heating rate; and (e) generating a thermogram.

Clause 19. The process of Clause 17 or Clause 18, wherein the adsorbentcomprises a microporous particle, a nanoporous particle, a mesoporousparticle, or a combination thereof.

Clause 20. The process of any one of Clauses 17 to 19, wherein theadsorbent comprises a mesoporous particle.

Clause 21. The process of any one of Clauses 17 to 20, wherein theadsorbent comprises silica.

Clause 22. The process of any one of Clauses 17 to 21, furthercomprising evacuating the system prior to introducing the substance intothe sample cell.

Clause 23. The process of any one of Clauses 17 to 22, furthercomprising: performing operations (a)-(e), wherein operation (b) isperformed at a second initial pressure, the second initial pressurebeing different from the first initial pressure.

Clause 24. The process of any one of Clauses 17 to 23, furthercomprising: performing operations (a)-(e) at a series of initialpressures, the initial pressures being different from each other andfrom the first and second initial pressures.

Clause 25. The process of any one of Clauses 17 to 24, wherein thesubstance is a pure substance.

Clause 26. The process of any one of Clauses 17 to 24, wherein thesubstance is a substantially pure substance.

Clause 27. The process of any one of Clauses 17 to 24, wherein thesubstance is more than one compound.

Clause 28. The process of any one of Clauses 17 to 24, wherein thesubstance is a gas at 25° C. and 1 atm.

Clause 29. The process of any one of Clauses 17 to 24, wherein thesubstance is a liquid at 25° C. and 1 atm.

Clause 30. The process of any one of Clauses 17 to 29, wherein when theprocess includes cooling the substance at a cooling rate, the coolingrate is from about 0.01° C./min to about 1° C./min, or from about 0.01°C./min to about 0.5° C./min, or from about 0.01° C./min to about 0.1°C./min; or wherein when the process includes heating the substance at aheating rate, the heating rate is from about 0.01° C./min to about 1°C./min, or from about 0.01° C./min to about 0.5° C./min, or from about0.01° C./min to about 0.1° C./min.

Clause 31. The process of any one of Clauses 17 to 30, wherein when theprocess includes cooling the substance at a cooling rate, the coolingrate is about 0.03° C./min; or wherein when the process includes heatingthe substance at a cooling rate, the heating rate is about 0.03° C./min.

Clause 32. The process of any one of Clauses 17 to 31, wherein thesubstance comprises a hydrocarbon (such as a C₁-C₂₀ unsubstitutedhydrocarbon, such as a C₁-C₁₀ unsubstituted hydrocarbon), a substitutedhydrocarbon (such as a C₁-C₂₀ substituted hydrocarbon, such as a C₁-C₁₀substituted hydrocarbon), or a combination thereof.

Clause 33. The process of any one of Clauses 17 to 32, wherein thesubstance comprises methane, ethane, methanol, or a combination thereof.

Clause 34. The process of any one of Clauses 17 to 33, wherein thesubstance comprises a gas such as Na, SO₂, Ar, a carbon containing gas(such as CO and/or CO₂), or a combination thereof.

Clause 35. The process of any one of Clauses 17 to 34, furthercomprising determining the conditions (e.g., a pressure and atemperature) of the substance's phase transition based on thethermogram.

Clause 36. A process for measuring a vapor-liquid transition of asubstance in a constant volume system, comprising: (a) introducing asubstance into a sample cell of a calorimetric block of a differentialscanning calorimeter (DSC) at a first initial pressure, the systemvolume being constant, and the substance comprises a hydrocarbon, asubstituted hydrocarbon, a carbon containing gas, or a combinationthereof, (b) maintaining the substance in a vapor phase; (c) cooling thesubstance at a cooling rate of about 1° C./min or less; and (d)generating a thermogram.

Clause 37. A process for measuring a vapor-liquid transition of asubstance in a constant volume system, comprising: (a) introducing asubstance into a sample cell of a calorimetric block of a differentialscanning calorimeter (DSC) at a first initial pressure, the systemvolume being constant and the substance comprises a hydrocarbon, asubstituted hydrocarbon, a carbon containing gas, or a combinationthereof, (b) maintaining the substance in a liquid phase; (c) heatingthe substance at a heating rate of about 1° C./min or less; and (d)generating a thermogram.

Clause 38. The process of Clause 36 or Clause 37, further comprisingintroducing an adsorbent into the sample cell prior to introducing thesubstance into the sample cell.

Clause 39. The process of any one of Clauses 36 to 38, wherein theadsorbent comprises a microporous particle, a nanoporous particle, amesoporous particle, or a combination thereof.

Clause 40. The process of any one of Clauses 36 to 39, wherein theadsorbent comprises a mesoporous particle.

Clause 41. The process of any one of Clauses 36 to 40, wherein theadsorbent comprises silica.

Clause 42. The process of any one of Clauses 36 to 41, furthercomprising evacuating the system prior to introducing the substance intothe sample cell.

Clause 43. The process of any one of Clauses 36 to 42, furthercomprising: performing operations (a)-(d), wherein operation (a) isperformed at a second initial pressure, the second initial pressurebeing different from the first initial pressure.

Clause 44. The process of any one of Clauses 36 to 43, furthercomprising: performing operations (a)-(d) at a series of initialpressures, the initial pressures being different from each other andfrom the first and second initial pressures.

Clause 45. The process of any one of Clauses 36 to 44, wherein thesubstance is a pure substance.

Clause 46. The process of any one of Clauses 36 to 44, wherein thesubstance is a substantially pure substance.

Clause 47. The process of any one of Clauses 36 to 44, wherein thesubstance is more than one compound.

Clause 48. The process of any one of Clauses 36 to 44, wherein thesubstance is a gas at 25° C. and 1 atm.

Clause 49. The process of any one of Clauses 36 to 44, wherein thesubstance is a liquid at 25° C. and 1 atm.

Clause 50. The process of any one of Clauses 36 to 49, wherein when theprocess includes cooling the substance at a cooling rate, the coolingrate is from about 0.01° C./min to about 1° C./min, or from about 0.01°C./min to about 0.5° C./min, or from about 0.01° C./min to about 0.1°C./min; or wherein when the process includes heating the substance at aheating rate, the heating rate is from about 0.01° C./min to about 1°C./min, or from about 0.01° C./min to about 0.5° C./min, or from about0.01° C./min to about 0.1° C./min.

Clause 51. The process of any one of Clauses 36 to 50, wherein when theprocess includes cooling the substance at a cooling rate, the coolingrate is about 0.03° C./min; or wherein when the process includes heatingthe substance at a cooling rate, the heating rate is about 0.03° C./min.

Clause 52. The process of any one of Clauses 36 to 51, wherein thesubstance comprises a hydrocarbon (such as a C₁-C₂₀ unsubstitutedhydrocarbon, such as a C₁-C₁₀ unsubstituted hydrocarbon), a substitutedhydrocarbon (such as a C₁-C₂₀ substituted hydrocarbon, such as a C₁-C₁₀substituted hydrocarbon), or a combination thereof.

Clause 53. The process of any one of Clauses 36 to 53, wherein thesubstance comprises methane, ethane, methanol, or a combination thereof.

Clause 54. The process of any one of Clauses 36 to 54, wherein thesubstance comprises a gas such as N₂, SO₂, Ar, a carbon containing gas(such as CO and/or CO₂), or a combination thereof.

Clause 55. A process for measuring a vapor-liquid transition of asubstance in a constant volume system, comprising (a) introducing asubstance into a sample cell of a calorimetric block of a differentialscanning calorimeter (DSC) at a first initial pressure, the systemvolume being constant and the substance comprises a hydrocarbon, asubstituted hydrocarbon, a carbon containing gas, a non-carboncontaining gas, or a combination thereof, and optionally introducing anadsorbent into the sample cell prior to introducing the substance intothe sample cell; (b) maintaining the substance in a vapor phase; (c)cooling the substance at a cooling rate of about 1° C./min or less; and(d) generating a thermogram.

Clause 56. A process for measuring a vapor-liquid transition of asubstance in a constant volume system, comprising (a) introducing asubstance into a sample cell of a calorimetric block of a differentialscanning calorimeter (DSC) at a first initial pressure, the systemvolume being constant and the substance comprises a hydrocarbon, asubstituted hydrocarbon, a carbon containing gas, or a combinationthereof, and optionally introducing an adsorbent into the sample cellprior to introducing the substance into the sample cell; (b) maintainingthe substance in a liquid phase; (c) heating the substance at a heatingrate of about 1° C./min or less; and (d) generating a thermogram.

Clause 57. The process of Clause 55 or Clause 56, further comprisingintroducing an adsorbent into the sample cell prior to introducing thesubstance into the sample cell.

Clause 58. The process of any one of Clauses 55 to 57, wherein theadsorbent comprises a microporous particle, a nanoporous particle, amesoporous particle, or a combination thereof.

Clause 59. The process of any one of Clauses 55 to 58, wherein theadsorbent comprises a mesoporous particle.

Clause 60. The process of any one of Clauses 55 to 59, wherein theadsorbent comprises silica.

Clause 61. The process of any one of Clauses 55 to 60, furthercomprising evacuating the system prior to introducing the substance intothe sample cell.

Clause 62. The process of any one of Clauses 55 to 61, furthercomprising: performing operations (a)-(d), wherein operation (a) isperformed at a second initial pressure, the second initial pressurebeing different from the first initial pressure.

Clause 63. The process of any one of Clauses 55 to 62, furthercomprising: performing operations (a)-(d) at a series of initialpressures, the initial pressures being different from each other andfrom the first and second initial pressures.

Clause 64. The process of any one of Clauses 55 to 63, wherein thesubstance is a pure substance, or wherein the substance is asubstantially pure substance, or wherein the substance is more than onecompound, or wherein the substance is a gas at 25° C. and 1 atm, orwherein the substance is a liquid at 25° C. and 1 atm.

Clause 65. The process of any one of Clauses 55 to 64, wherein when theprocess includes cooling the substance at a cooling rate, the coolingrate is from about 0.01° C./min to about 1° C./min, or from about 0.01°C./min to about 0.5° C./min, or from about 0.01° C./min to about 0.1°C./min; or wherein when the process includes heating the substance at aheating rate, the heating rate is from about 0.01° C./min to about 1°C./min, or from about 0.01° C./min to about 0.5° C./min, or from about0.01° C./min to about 0.1° C./min.

Clause 66. The process of any one of Clauses 55 to 65, wherein when theprocess includes cooling the substance at a cooling rate, the coolingrate is about 0.03° C./min; or wherein when the process includes heatingthe substance at a cooling rate, the heating rate is about 0.03° C./min.

Clause 67. The process of any one of Clauses 55 to 66, wherein when thesubstance comprises a hydrocarbon, the hydrocarbon is a C₁-C₂₀unsubstituted hydrocarbon, such as a C₁-C₁₀ unsubstituted hydrocarbon,or a combination thereof; or wherein when the substance comprises asubstituted hydrocarbon, the substituted hydrocarbon is a C₁-C₂₀substituted hydrocarbon, such as a C₁-C₁₀ substituted hydrocarbon, or acombination thereof; or a combination thereof.

Clause 68. The process of any one of Clauses 55 to 67, wherein when thesubstance comprises a hydrocarbon, the hydrocarbon is methane, ethane,or a combination thereof, or wherein when the substance comprises asubstituted hydrocarbon, the substituted hydrocarbon, wherein when thesubstance comprises a carbon containing gas, the carbon containing gasis CO, CO₂, or a combination thereof, or wherein when the substancecomprises a non-carbon containing gas, the non-carbon containing gas isN₂, SO₂, Ar, or a combination thereof.

EXAMPLES A. Measuring the Onset of the Vapor-Liquid Phase Transition inBulk—Isochoric Dew-Point Measurement Vapor Pressure of CO₂

Vapor pressures of CO₂ are measured using the isochoric dew-pointmeasurement. An example thermogram of the vapor pressure measurement ofCO₂ using the isochoric dew-point measurement method, along with thepressure history, is shown in FIG. 2A. The temperature curve is astraight line with a constant slope throughout the process because aconstant cooling rate can be used. Prior to the phase transition fromvapor to liquid, the pressure of the test vessel declines graduallybecause of the decreasing temperature in the closed system. When a phasetransition from vapor to liquid occurs, heat is released from the testsample, leading to a sharp increase in the heat flow curve, as shown inFIG. 2A. At the same time, the pressure of the system starts to decreasefaster due to condensation. The onset condition of the phase transitionis determined from the intersection point between the baseline and thetangent line (the dashed line) of the rising part of the exothermic peak(point A). The condensation temperature (point B) and vapor pressure(point C) can be determined by drawing a vertical line through point A.

FIG. 2B shows the result of four individual measurements of vaporpressures of CO₂, Examples 1-4, measured using the isochoric dew-pointmeasurement method described herein relative to a comparative data set,Comparative 1. The cooling paths of the experiments, which are theisochores, are also shown. The four isochoric dew-point measurementswere varied by the initial pressure at which the CO₂ was introduced intothe sample cell. The comparative data set is data from the NationalInstitute of Standards and Technology (NIST). The NIST data set is theresult of critical evaluations of data obtained by several differentsources which have been fitted to a mathematical function. FIG. 2Bdemonstrates that the vapor pressures obtained using the isochoricdew-point measurements are in excellent agreement with the comparativeNIST data, with an average absolute deviation of less than about 1%.

Operators using conventional isobaric methods, such as the isobaricmethod described in ASTM E1782, would be unable to measure (or, at thevery least, would have great difficulty in measuring) the vapor pressureof substances, such as CO₂, for at least the reason that finding aninert gas (or non-reactive gas) that dissolves only sparingly in CO₂ ischallenging. The inert or non-reactive gas is added to the sample cellfor typical isobaric methods in order to maintain the pressure in thesample cell. Furthermore, substances such as CO₂ are volatile, or evenhighly volatile. Further difficulties in typical isobaric measurementsare encountered when determining several measurement parameters, e.g.,the size of the test sample and the size of the pinhole, both of whichshould also be optimized together with the scanning rate (theheating/cooling rate). When these parameters are not optimized, thebaseline of the thermogram becomes unclear and the measurements are notaccurate. In contrast, the isochoric measurements described herein caneliminate most, if not all, of these difficulties. The baseline of thethermogram generated is also clear and the onset of the phase transitioncan be determined easily.

The isochoric dew-point measurement method described herein can also beused to determine the vapor pressure curve of a substance in onecontinuous experiment. For the continuous measurements, the coolingprocess of the sample is continued after condensation has occurred. FIG.3 shows the results from the a continuous isochoric dew-pointmeasurement of the vapor pressure curve of CO₂, Example 5, relative toComparative 1. Proper selection of the scanning rate can ensure thatequilibrium conditions can be achieved and/or maintained at pointsduring the cooling process. After reaching the dew point, the vaporremains in equilibrium with the liquid upon further cooling, as drop bydrop of liquid forms, provided the cooling rate is so low (such as lessthan 0.1° C./min) that equilibrium conditions can be achieved and/ormaintained at points during the cooling process. For the measurementsshown in FIG. 3 , the cooling rate is about 0.03° C./min. With a coolingrate of 0.03° C./min, equilibrium conditions can be achieved at anypoint during the cooling process. FIG. 3 demonstrates that ifequilibrium conditions can be achieved at a point during the coolingprocess, the vapor-pressure curve can be generated continuously. Theisochoric process can be stopped at specified temperatures which canenable the measurement of vapor pressure at a certain temperature.

Dew Points of a Methane/Ethane Gas Mixture

Dew points at different pressures or temperatures for a methane/ethane(CH₄/C₂H₆) gas mixture (about 15±0.3% CH₄ and 85±0.3% C₂H₆) are measuredusing the isochoric dew-point measurement. A typical thermogram of thisdew-point measurement is shown in FIG. 4A. The onset condition of thephase transition is determined from the intersection point between thebaseline and the tangent line (the dashed line) of the rising part ofthe exothermic peak (point A). The dew-point temperature (point B) anddew-point pressure (point C) can be determined by drawing a verticalline through point A.

FIG. 4B shows the data obtained for the dew points of four individualmeasurements of the methane/ethane gas mixture using the isochoricdew-point measurement method described herein, Examples 6-9, relative tocomparative data, Comparative 2. The cooling paths of the experimentsare also shown. The four isochoric dew-point measurements were varied bythe initial pressure at which the methane/ethane gas mixture wasintroduced into the sample cell. The comparative data is on a gasmixture of 14.98% methane and 85.02% ethane. The data obtained by theisochoric method described herein is in excellent agreement with thecomparative data. The experimental error of the comparative data is±0.136 bar or ±0.167° C., whichever is larger, if the methane/ethanecomposition is considered exact. Neglecting the errors of thecomparative data and using the comparative data as the standard values,the average absolute deviation of dew-point pressures measured by theisochoric method described herein is about 1.36%. By considering theuncertainty of the gas composition used for the isochoric measurementsand the accuracy of the pressure transducer of the DSC apparatus, theerror in the dew-point pressure of the isochoric measurements isestimated to be about ±0.25 bar. Although the method is demonstrated fora binary gas mixture, it can be used to measure the dew points of gasmixtures comprising two or more gases.

The isochoric dew-point measurement, in which the occurrence of thefirst drop of liquid phase is determined during a cooling isochoricprocess, is used to measure the vapor pressures of pure substances(e.g., CO₂) at different boiling temperatures and the dew points of amethane/ethane gas mixture at different pressures or temperatures.

The isochoric method is therefore demonstrated to be superior to theconventional isobaric method for phase-transition measurements usingDSC. In all of these isochoric methods, there is no need to determineseveral measurement parameters usually encountered in the isobaricmethod, e.g., the size of the test sample, the size of the pinhole, andthe associated scanning rate. The baseline of the thermogram generatedis also clear and the onset of the phase transition can be determinedeasily. The isochoric method can be used to measure the onset ofvapor-liquid phase transition for a wide range of substances andmixtures, including the ones for which the isobaric method isinapplicable. Conventional isobaric methods are unable to measure thedew points of the gaseous system because, e.g., the gases may escapethrough the pinhole of the sample cell leading to altered compositionalprofiles. This can lead to altered composition profiles. In contrast,the isochoric method described herein can be used to measure the gassystem and the measurements are more accurate than conventional methodsto measure gas systems.

B. Measuring the Onset of the Vapor-Liquid Phase Transition inNanopores—Isochoric Dew-Point Measurement

SBA-15 mesoporous silica is used as a non-limiting example of anadsorbent to test the isochoric method described herein. SBA-15 withthree different pore diameters, S1, S2, and S3, were purchased and usedwithout further treatment. Properties of SBA-15 samples are shown inTable 1.

TABLE 1 Sample S_(BET) (m²/g) V_(total) (cm³/g) D_(BJH) (nm) S1 746.70.738 3.408 S2 803.1 0.859 4.892 S3 772.6 1.202 6.563

Capillary Condensation Measurements of CO₂ in SBA-15

The capillary condensation of CO₂ in the SBA-15 mesoporous silicasamples is measured using the isochoric dew-point measurement methoddescribed herein. FIG. 5A shows an example thermogram and pressurehistory of the capillary condensation of CO₂ in SBA-15 as well as thebulk condensation of CO₂. The thermogram shows a small exothermic peakdue to the phase transition of CO₂ occurring in the pores and a largerexothermic peak due to the bulk condensation of CO₂. Before the phasetransition occurs in the pores, the pressure of the test vesseldecreases gradually because of the decreasing temperature present in theclosed system. When condensation occurs within the pores, heat isreleased from the test sample, leading to a small exothermic peak in theheat flow curve, and the pressure of the system decreases more quicklyto a lower level. As the cooling process continues, the pressuredecreases gradually due to the decreasing temperature in the system.When the bulk condensation eventually starts to occur, the pressureagain drops faster and at the same time a larger amount of heat isreleased, leading to a sharp increase of the heat flow curve. Along acooling path, the phase transition of confined fluids in nanopores isencountered first before that of the bulk fluid. Notably, the isochoricdew-point procedure is able to measure both capillary and bulkcondensation in a single run.

The onset condition of the bulk phase transition can be determined fromthe intersection point between the baseline and the tangent line (thedashed line) of the rising part of the exothermic peak (point A). Thecondensation temperature (point B) and vapor pressure (point C) can bedetermined by drawing a vertical line through point A.

To determine the onset condition for capillary condensation, unlike thedetermination of the onset condition of the bulk phase transition, onedoes not take the intersection point between the heat flow baseline andthe tangent line of the rising part of the peak to define the capillarycondensation because such an intersection point gives the conditions ofcondensation that occurs in the smallest mesopores only, not the entiremesopores that have an effective diameter corresponding to the peak ofpore size distribution, DBJH. Instead, the onset condition of thecapillary condensation is determined by drawing a vertical dashed linethat intersects the maximum of the thermogram peak (point A′), thetemperature history, and the pressure history, which provides thecondensation temperature (point B′) and vapor pressure (point C′) of thecondensation. The maximum of this thermogram peak occurs simultaneouslywith the largest time rate of change of the system pressure during thecapillary condensation, which indicates that with the amount ofadsorbent and cooling rate used, there is no apparent time lag betweenthe heat flow and pressure measurements. Since the temperature andpressure measurements are done using different devices, this is showsthat the measurements of temperature and pressure of the phasetransition are accurate. Temperature is measured by the temperaturesensor of the DSC, while pressure is measured by using a pressure sensoroutside the DSC.

The effect of scanning rate on the isochoric measurements in thepresence of the adsorbent, S3, is shown in FIG. 5B. Table 2 showscertain conditions for the four isochoric experiments in FIG. 5B. Onlyfour isochoric experiments are needed since the procedure can measurethe bulk phase transition (Examples 10A, 11A, 12A, and 13A)simultaneously with that of the confined fluid (Examples 10B, 11B, 12B,and 13B).

TABLE 2 Amount of Scanning Rate Example Adsorbent S3 (mg) (° C./min)10A, 10B 7.5 0.1 11A, 11B 3 0.1 12A, 12B 1 0.1 13A, 13B 7.5 0.03

In FIG. 5B, the dashed lines are added to trace an example capillarycondensation curve, and the cooling paths are shown only for somemeasurements. Measurements with S3 using two different coolingrates—0.1° C./min and 0.03° C./min—show that the measured vaporpressures of bulk CO₂ are in agreement with the comparative NIST data,Comparative 3, and the measured conditions for capillary condensationare consistent and fall on the same curve. Note that the ability of theprocedure to measure the bulk phase transition provides a robust way ofverifying the accuracy of the measurements. The data also shows that ahigher scanning rate of 0.1° C./min can be used for faster measurements.

The effect of the amount of adsorbent used on the isochoric measurementsis also shown in FIG. 5B. FIG. 5B shows that the amount of adsorbent canhave little to no effect on the capillary condensation of CO₂. As shownbelow, a different conclusion can be reached for the capillarycondensation of gas mixtures.

FIG. 5C shows the results of the isochoric dew-point measurements of thecapillary condensation in SBA-15 samples and bulk condensation of CO₂relative to comparative data. The comparatives are NIST data(Comparative 4) and data from the capillary condensation of CO₂ inMCM-41 (4.4 nm and 3.7 nm) (Comparatives 5 and 6). Table 3 shows certainconditions for the three isochoric experiments in FIG. 5C. Only threeisochoric experiments are needed since the procedure can measure thebulk phase transition (Examples 14A, 15A, and 16A) simultaneously withthat of the confined fluid (Examples 14B, 15B, and 16B).

TABLE 3 Type of Amount of Scanning Rate Example Adsorbent Adsorbent (mg)(° C./min) 14A, 14B S1 7.5 0.1 15A, 15B S2 7.5 0.1 16A, 16B S3 7.5 0.1

In FIG. 5C, the dashed lines are added to trace an example capillarycondensation curve, and the cooling paths are shown only for somemeasurements for clarity. The bulk vapor pressures obtained using theisochoric dew-point measurements described herein are in excellentagreement with the NIST data. The measurements demonstrate that thephase transition in the pores happens at a higher temperature than thatin the bulk on a cooling path. These results also confirm that the phasetransition curve of fluids confined in a smaller pore is below that in alarger pore on the phase diagram. The capillary condensation in SBA-15is different from that of MCM-41. Although not wishing to be bound byany theory, the difference may be attributed to the existence ofmicropores in SBA-15.

Dew Point Measurements of a Methane/Ethane Gas Mixture in SBA-15

The same isochoric procedure as that for pure fluids is applied tomeasure the dew points of a methane/ethane gas mixture in nanopores at abulk composition of about 15±0.3% CH₄/85±0.3% C₂H₆. FIG. 6A shows anexample thermogram of the capillary condensation and bulk condensationof the gas mixture for such a measurement. The thermogram analysis ofthis dew-point measurement is also the same as that of capillarycondensation measurement of CO₂. Because the real composition of the gasmixture in the pores cannot be measured, it is common practice to reportthe measureable conditions of the confined phase transition based on thecomposition of the bulk mixture surrounding the pores. Thus, the dewpoint of the confined mixture here is defined as the onset of phasetransition in the pores at a fixed composition of the surrounding bulkgas mixture.

The onset condition of the bulk phase transition can be determined fromthe intersection point between the baseline and the tangent line (thedashed line) of the rising part of the exothermic peak (point A). Thedew-point temperature (point B) and dew-point pressure (point C) can bedetermined by drawing a vertical line through point A. The onsetcondition for capillary condensation is determined by drawing a verticaldashed line that intersects the maximum of the thermogram peak (pointA′), the temperature history, and the pressure history, which providesthe dew-point temperature (point B′) and dew-point pressure (point C′)of the condensation.

It is well known that the presence of nanopores may alter the bulk gascomposition by selective adsorption. Hence, the measured phasetransition in the pores would not represent that of confined mixturesurrounded by a bulk having the initial composition. The experiments areset up to make the bulk composition change before and after thecapillary condensation negligible so that the subsequent bulkcondensation that occurs upon further cooling can be compared with thatof the bulk without the adsorbent. A match between them providesevidence that the bulk composition is effectively unchanged. One way tominimize the alteration of the bulk composition is to employ a smallamount of the adsorbent. The suitable amount of adsorbent issystem-specific, varying for different fluids and different adsorbents.If a relatively large amount of adsorbent is used, the thermogram peakof the dew point of gas mixture in pores can be higher, and easy toidentify, but the bulk gas composition can significantly change becauseof the selective adsorption in the pores during the cooling process. Onthe other hand, if a smaller amount of adsorbent is used, the change inbulk gas composition is negligible, but the thermogram peak might not bedetectable. Therefore, an amount of adsorbent can be selected such thatit introduce both detectable thermogram peak and negligible change inbulk composition.

FIG. 6B shows the effect of the amount of S3 adsorbent used on themeasured dew points of the confined and bulk methane/ethane gas mixtures(15±0.3% CH_(4/85±0.3)% C₂H₆) for various examples. Comparative data,Comparative 7, for bulk bubble points and dew points of a gas mixture(14.98% methane and 85.02% ethane) is also shown. Table 4 shows certainconditions for the four isochoric experiments in FIG. 6B. Four isochoricexperiments are utilized since the procedure can measure the bulk phasetransition (Examples 17A, 18A, 19A, and 20A) simultaneously with that ofthe confined fluid (Examples 17B, 18B, 19B, and 20B).

TABLE 4 Amount of Scanning Rate Example Adsorbent S3 (mg) (° C./min)17A, 17B 1.3 0.1 18A, 18B 2.5 0.1 19A, 19B 7 0.1 20A, 20B 1.3 0.03

In FIG. 6B, the dashed lines are added to trace an example capillarycondensation curve, and the cooling paths are shown only for somemeasurements for clarity. Even an adsorbent amount as little as about2.5 mg changes the bulk gas composition appreciably. The presence ofnanopores shifts the measured bulk dew points to lower temperaturesbecause ethane is preferentially adsorbed during the process, and themeasured dew points of the confined mixtures do not represent thosesurrounded by the 15±0.3% CH₄/85±0.3% C₂H₆ bulk gas mixture. With about1.3 mg of adsorbent, on the other hand, even after capillarycondensation, the change in bulk gas composition is not noticeable,e.g., the original bulk dew points can still be reproduced. Therefore,about 1.3 mg of adsorbent is used to generate accurate data for S3.Similarly, accurate data can be generated by using adsorbent amounts ofabout 2.2 mg and about 2.0 mg for 51 and S2, respectively (not shown inFigure). Therefore, in the measurements of dew points of fluid mixturesin the pores, the change in the bulk gas composition due to selectiveadsorption and capillary condensation can be mitigated using a suitableamount of adsorbent that varies for different fluids and adsorbents.

FIG. 6B also shows the effects of scanning rate on the DSC measurementsof dew points of the methane/ethane gas mixture in about 1.3 mg of S3.The bulk composition of the methane/ethane gas mixture is about 15±0.3%CH₄/85±0.3% C₂H₆. Measurements with S3 using two different coolingrates—0.1° C./min and 0.03° C./min—show that the measured bulk dewpoints fall on the dew-point curve obtained from comparative data.Similar to capillary condensation measurements of CO₂, a higher scanningrate of 0.1° C./min can be used for faster measurements.

FIG. 6C shows the results of the dew-point measurements of the confinedand bulk methane/ethane gas mixtures (15±0.3% CH₄/85±0.3% C₂H₆) forvarious examples. Comparative data, Comparative 8, is also shown. Thecomparative data of bulk bubble points and dew points are of a gasmixture (14.98% methane and 85.02% ethane) in adsorbent. Table 5 showscertain conditions for the four isochoric experiments in FIG. 6C. Threeisochoric experiments are utilized since the procedure can measure thebulk phase transition (Examples 21A, 22A, and 23A) simultaneously withthat of the confined fluid (Examples 21B, 22B, and 23B).

TABLE 5 Type of Amount of Scanning Rate Example Adsorbent Adsorbent (mg)(° C./min) 21A, 21B S1 2.2 0.1 22A, 22B S2 2.0 0.1 23A, 23B S3 1.3 0.1

In FIG. 6C, the dashed lines are added to trace an example capillarycondensation curve, and the cooling paths are shown only for somemeasurements for clarity. Similar to the capillary condensation of purefluids, the dew-point curve of fluid mixtures confined in nanopores isalso below that of the surrounding bulk fluid, and the curve is evenlower for smaller pores on the phase diagram. The results show that thephase transition boundaries of fluids in nanopores are below those ofthe bulk fluids and that the boundaries of fluids in a smaller pore arebelow those in a larger pore on the phase diagram.

The isochoric dew-point measurement method provides an efficient andaccurate measurement of the phase transition of pure fluids and fluidmixtures in nanopores. In addition, the procedure enables themeasurement of the bulk phase transition simultaneously with that of theconfined fluids. The unique ability of the procedure to measure the bulkphase transition simultaneously with that of the confined fluidsprovides a robust way of verifying the accuracy of the measurements.

C. Measuring the Onset of the Vapor-Liquid Phase Transition inBulk—Isochoric Evaporation-Point Measurement

An example thermogram of the measurement of the evaporation of CO₂ inthe bulk phase using this isochoric evaporation-point measurementmethod, along with the pressure history, is shown in FIG. 7A. Thetemperature curve is a straight line with a constant slope throughoutthe process because a constant cooling rate can be used. The heat flowis at first stable, showing a flat baseline, and then the occurrence ofa phase transition (evaporation) in the test vessel results in anendothermic peak in the heat flow due to the absorption of heat duringthe evaporation process. The system pressure increases gradually atfirst because of the temperature increase in the system and increasesmuch faster after evaporation as a consequence of the additional vaporphase generated in the system. The slope change in the pressure curvecorresponds to the abrupt fall in heat flow, which indicates that withthe heating rate used, there is no apparent time lag between the heatflow and pressure measurement. The onset condition of evaporation isdetermined from the intersection between the baseline and the tangentline to the incline portion of the endothermic peak (Point A). Theboiling temperature (Point B) and vapor pressure (Point C) can bedetermined by drawing a vertical line through point A.

FIG. 7B shows the result of five individual measurements of evaporationof CO₂ in the bulk phase, Examples 26-30, and ethane in the bulk phase,Examples 31-35, using the isochoric evaporation point measurement methoddescribed herein. FIG. 7B also shows a comparative data set, Comparative9 and 10, for CO₂ and ethane, respectively. The heating paths of theexperiments, which are the isochores, are also shown. The five isochoricdew-point measurements for each substance were varied by the initialpressure at which the CO₂ or ethane was introduced into the sample cell.The comparative data set is data from the National Institute ofStandards and Technology (NIST). The NIST data set is the result ofcritical evaluations of data obtained by several different sources whichhave been fitted to a mathematical function. FIG. 7B demonstrates thatthe vapor pressures obtained using the isochoric dew-point measurementsare in excellent agreement with the comparative NIST data, with anaverage absolute deviation of about 0.22% for CO₂ and about 0.5% forethane. The errors of the temperature and pressure measurements areestimated to be about ±0.04° C. and about ±0.04 bar, respectively.

The isochoric evaporation-point method described herein overcomes thosesame hurdles described above presented by conventional isobaric methods(e.g., the ASTM method).

The isochoric evaporation-point measurement method described herein canalso be used to determine the vapor pressure curve of a substance in onecontinuous experiment. For the continuous measurements, the heatingprocess of the sample is continued after the first bubble has occurred.The thermogram of such a continuous measurement is shown in FIG. 8A. Thethermogram can be divided into three distinct stages separated by thetwo vertical dashed lines drawn in the figure. In the first stage, thefluid inside the test vessel is in a single liquid phase. With theincrease of the system temperature, evaporation occurs in the testvessel at the left-side vertical dashed line, thus entering the secondstage, i.e., vapor-liquid phase equilibrium. The pressure increases morequickly and heat flow deviates from the baseline in this stage. If thetemperature is further increased, the system reaches the right-sidevertical dashed line and enters the third stage, with the heat flowreturning to the base line and the pressure increasing slower again,which indicates that the fluid inside the test cell has been evaporatedand the system is in the vapor region.

FIG. 8B shows the results of continuous measurements with CO₂ (Example34) and ethane (Example 35) using the isochoric evaporation-pointmeasurement method. Both measurements start in the liquid region. Withthe increase of the system temperature, the heating path hits the vaporpressure curve at Point 1, whose coordinate can be determined fromPoints B and C in FIG. 8A. Point 1 indicates the appearance of the firstbubble of vapor in the liquid sample, namely the onset of evaporation.Then the heating path follows the vapor pressure curve continuouslyuntil all of the liquid in the test vessel is evaporated at Point 2. Inother words, Point 2 indicates the disappearance of the last drop ofliquid in the test vessel. The coordinate of Point 2 can be determinedfrom Points B′ and C′ in FIG. 8A, with a procedure similar to thedetermination of Point 1. For the measurements shown in FIG. 8B, thecooling rate is about 0.03° C./min. With a cooling rate of 0.03° C./min,equilibrium conditions can be achieved at any point during the coolingprocess. FIG. 8B demonstrates that if equilibrium conditions can beachieved at any point during the heating process, the vapor pressurecurve can be generated continuously. Of note, by adding the small glassbar into the test vessel, the distance between Points 1 and 2 can beeffectively decreased, thus entering the vapor region at a lowertemperature and pressure with the same initial conditions.

The isochoric method is therefore demonstrated to be superior to theconventional isobaric method for phase-transition measurements usingDSC. In all of these isochoric methods, there is no need to determineseveral measurement parameters usually encountered in the isobaricmethod, e.g., the size of the test sample, the size of the pinhole, andthe associated scanning rate. The baseline of the thermogram generatedis also clear and the onset of the phase transition can be determinedeasily. The isochoric method can be used to measure the onset ofvapor-liquid phase transition for a wide range of substances andmixtures, including the ones for which the isobaric method isinapplicable. Conventional isobaric methods are unable to measure theevaporation points of the volatile liquid system because, e.g., vapormay escape through the pinhole of the sample cell leading to unclearbaseline in the thermogram. In contrast, the isochoric method describedherein can be used to measure the volatile liquid system and themeasurements are more accurate than conventional methods.

D. Measuring the Onset of the Vapor-Liquid Phase Transition inNanopores—Isochoric Evaporation-Point Measurement

The capillary evaporation of CO₂ and ethane in two different pore sizesof SBA-15, adsorbent S2 and S3, is measured using the isochoricevaporation-point measurement method described herein.

FIG. 9A shows an example thermogram and pressure history of themeasurement of capillary evaporation of CO₂ in nanoporous media. FIG. 9Ais similar to FIG. 8A, except that a small endothermic peak in the heatflow due to capillary evaporation of fluid in the nanoporous media. Thissmall peak is located in the vapor region of the bulk fluid, which canindicate that capillary evaporation occurs after all of the liquidoutside the pore, namely in the bulk phase, has been evaporated. Inother words, evaporation inside the pore should occur at a highertemperature (isobarically) or a lower pressure (isothermally), and beindependent of the evaporation outside the pore. The capillaryevaporation point is determined using a similar procedure as thedetermination of capillary condensation described above. Specifically, aline parallel to the heat flow baseline, which is tangent to theendothermic peak at Point A″, is drawn (dotted line in FIG. 9A). Thendrawing a vertical dashed line that passes through Point A″ provides thetemperature (Point B″) and pressure (Point C″) of capillary evaporation.

FIGS. 9B-9E shows the results of the isochoric evaporation-pointmeasurement method of the confined and bulk CO₂ and ethane in thepresence of adsorbent S2 and adsorbent S3. For comparison, experimentaldata of capillary condensation obtained for the same system(adsorbent+adsorbate) is included as well as comparative NIST data.Table 6 shows these examples and comparatives. The isochoricevaporation-point measurement method can measure the bulk phasetransition (Examples 36A-51A) simultaneously with that of the confinedfluid (Examples 36B-51B).

TABLE 6 Type of Amount of Scanning Rate Example Substance AdsorbentAdsorbent (mg) (° C./min) Comparative 13 CO₂ — — — Comparative 14 CO₂ S27.5 0.1 36A, 36B CO₂ S2 12.0 0.03 37A, 37B CO₂ S2 12.0 0.03 38A, 39B CO₂S2 12.0 0.03 39A, 39B CO₂ S2 12.0 0.03 Comparative 15 C₂H₆ — — —Comparative 16 C₂H₆ S2 7.5 0.1 40A, 40B C₂H₆ S2 12.0 0.03 41A, 41B C₂H₆S2 12.0 0.03 42A, 42B C₂H₆ S2 12.0 0.03 43A, 43B C₂H₆ S2 12.0 0.03Comparative 17 CO₂ — — — Comparative 18 CO₂ S3 7.5 0.1 44A, 44B CO₂ S38.0 0.03 45A, 45B CO₂ S3 8.0 0.03 46A, 46B CO₂ S3 8.0 0.03 47A, 47B CO₂S3 8.0 0.03 Comparative 19 C₂H₆ — — — Comparative 20 C₂H₆ S3 7.5 0.148A, 48B C₂H₆ S3 8.0 0.03 49A, 49B C₂H₆ S3 8.0 0.03 50A, 50B C₂H₆ S3 8.00.03 51A, 5 IB C₂H₆ S3 8.0 0.03 Comparatives 13, 15, 17, and 19 are NISTdata without an adsorbent. Comparatives 14, 16, 18, and 20 are capillarycondensation data obtained from the isochoric dew- point measurementmethod described herein.

The example capillary evaporation measurements and bulk evaporationmeasurements of CO₂ in SBA-15 (adsorbent S2) are shown in FIG. 9B, andthe example capillary evaporation measurements and bulk evaporationmeasurements of ethane in SBA-15 (adsorbent S2) is shown in FIG. 9C. Theexample capillary evaporation measurements and bulk evaporationmeasurements of CO₂ in SBA-15 (adsorbent S3) is shown in FIG. 9D, andthe example capillary evaporation measurements and bulk evaporationmeasurements of ethane in SBA-15 (adsorbent S3) is shown in FIG. 9E. InFIGS. 9B-9E, the dashed lines are added to trace an example capillaryevaporation curve, and the heating paths of one test are shown forclarity. The results show that the phase transition boundaries of fluidsin nanopores are below those of the bulk fluids and that the boundariesof fluids in a smaller pore are below those in a larger pore on thephase diagram.

The isochoric evaporation-point measurement method provides an efficientand accurate measurement of the phase transition of pure fluids innanopores. In addition, the procedure enables the measurement of thebulk phase transition simultaneously with that of the confined fluids.The unique ability of the procedure to measure the bulk phase transitionsimultaneously with that of the confined fluids provides a robust way ofverifying the accuracy of the measurements.

Test Methods

Before conducting the experiments, the DSC is calibrated using twostandard materials: deionized water and naphthalene. The naphthalene ispurchased from Sigma Aldrich and used without further purification. TheCO₂ gas is UHP grade with a purity greater than 99.97%, purchased fromUnited States Welding, Inc. The UHP-grade gas mixture of CH₄ and C₂H₆ ispurchased from Airgas and Air Liquide, with a mole percentage of about15±0.3% CH₄ and about 85±0.3% C₂H₆. The nitrogen gas used is alsopurchased from United States Welding, Inc., with a purity greater thanabout 99.5%.

The general setup 1000 for the equipment utilized to measure the vaporpressures of pure substance and the dew points of mixtures using theisochoric method is shown in FIG. 8 . The equipment includes a micro-DSC(μDSC) 1002 having a reference vessel 1004 and a test vessel 1006. Theequipment further includes a cooling circulator 1008 to assist withtemperature control, a pressure transducer 1010, a vacuum pump 1012, asyringe pump 1014, a gas cylinder(s) 1016 that can contain the substanceof interest, a sweeping gas circuit 1018 connected to another gascylinder (e.g., N₂) 1020 and a computer 1022.

A high-pressure SETARAM μDSC VII is used in this study. The HP μDSC canoperate under either vacuum, atmospheric, or pressurized conditions,with a pressure limit of 400 bar and a temperature range of about −45°C. to about 120° C. Its sensitivity, as provided by SETARAM Inc., ishigh with a resolution of about 0.04 μW. The system temperature iscontrolled by using advanced Peltier cooling and heating principle withthe assistance of an auxiliary cooling circulator. Two gas-tighthigh-pressure vessels made of Hastelloy C₂₇₆, with the same volume ofabout 1 cm³, are used for each experiment. One is for reference, whichis generally empty, and the other contains the test sample.

A highly-sensitive digital pressure transducer manufactured by Mensor(CPT6100), calibrated using a modular pressure controller (GE DruckPACE6000) with the calibration software WIKA-Cal provided by Mensor, isused to measure the pressure of the test vessel. The transducer has apressure range of about 0 bar to about 414 bar with an accuracy of about0.01% of full span. The pressure data are acquired synchronously withthe heat flow data from μDSC. To ensure accurate recordings of pressure,the distance between the pressure transducer and the test vessel can beminimized. To further mitigate the temperature gradient within the testsystem as a result of heat transfer from or to the surrounding viatubing connecting the pressure transducer and the test vessel, aninsulator can be used.

A rotary vane vacuum pump (DUO 10 M) from PFEIFFER VACUUM is used toevacuate the sample vessel and a high-pressure syringe pump with adigital controller (260D) from TELEDYNE ISCO is used to inject the gasinto the test vessel and adjust the pressure to a desired value. Thesyringe pump has a cylinder capacity of about 266.05 mL and can be usedfor a pressure of up to about 517 bar. The pump has three delivery modes(constant flow, constant pressure, and dispense modes) and one refillmode, with an adjustable flow rate from about 0.001 mL/min to about 107mL/min.

A digital cooling circulator with a digital temperature controller fromVWR is connected directly to the μDSC to ensure the removal of heat fromthe two thermostatic walls, as well as to ensure the cooling of thepower rack placed in the instrument structure. An analytical balance(TE214S) from Sartorius is used to weigh the liquid sample, with anaccuracy of about ±0.1 mg, and a syringe is used to deliver the liquidsample into the test vessel.

Prior to each test, the test cell can be washed using deionized waterand dried in a drying oven at about 120° C. for about 2 hours. The testcell can be weighed to ensure that the cell is clean and completelydried.

Calibration of DSC

Although the feedback from SETARAM, as part of the apparatusmaintenance, shows that the HP μDSC used is in good condition for bothtemperature and heat measurement, e.g., for naphthalene, the measuredmelting point is about 80.54° C. (literature value: about 80.23° C.) andmeasured enthalpy of melting is about 148.012 J/g (literature value:about 147.6 J/g), a temperature correction procedure can be performed.Two standard materials with known melting points, e.g., water andnaphthalene, are employed to perform this temperature correction. Sincemelting point mainly varies according to the scanning rate used, themelting points of water and naphthalene are measured at three differentheating rates, e.g., about 0.05° C./min, about 0.1° C./min, and about0.5° C./min. The results are processed in a standard least squaresmethod to obtain the coefficients of the temperature correctionfunction, from which the temperature correction for any scanningtemperature and rate can be determined. All of these are done using thesoftware package provided by SETARAM Inc. After calibrating, the meltingpoints of water and naphthalene measured are about 0.01° C. and about80.267° C., respectively, at a scanning rate of about 0.03° C./min.

A. Measuring the Onset of the Vapor-Liquid Phase Transition inBulk—Isochoric Dew-Point Measurement

The isochoric dew-point measurement method was used for measuring thevapor pressure of CO₂ and the dew point of a CH₄/C₂H₆ mixture. The testsystem (the tubes and the test vessel inside the calorimetric block ofDSC) is first evacuated using a vacuum pump to remove the air from thesystem and to dry the system thoroughly. The substance of interest(e.g., the gas of interest) is then injected into the test vessel usinga syringe pump until a specified initial pressure is reached. Thereference vessel is blank. The test system is heated to a temperatureabove the saturation temperature or dew point temperature of thesubstance of interest and maintained at that temperature. Heating isused to help equilibrate the system, to help ensure that the test sampleis in the vapor phase, and to help ensure a stable pressure and heatflow baseline during the cooling operation. With a constant cooling rateof about 0.03° C./min, the system temperature is then decreased whilethe heat flow and pressure history are continuously recorded until anexothermic peak appears in the thermogram, after which the systemtemperature is restored to ambient conditions. The procedure is repeatedfor different initial pressures.

B. Measuring the Onset of the Vapor-Liquid Phase Transition inNanopores—Isochoric Dew-Point Measurement

The capillary condensation of CO₂ and the dew points of a gas mixture(methane/ethane) in SBA-15 mesoporous silica with different porediameters were measured using the isochoric dew-point procedure providedabove. The only difference is that for tests containing adsorbent, acertain amount of SBA-15 is first introduced into the test vessel usinga small spatula. Such amounts of SBA-15 are provided above. Theadsorbent is kept in a drying oven at about 120° C. for about 24 hoursprior to the test.

C. Measuring the Onset of the Vapor-Liquid Phase Transition inBulk—Isochoric Evaporation-Point Measurement

The isochoric evaporation-point measurement method was used to measuretemperature and pressure data of CO₂ and ethane. The test system (thetubes and the test vessel inside the calorimetric block of DSC) is firstevacuated using a vacuum pump to remove the air from the system and todry the system thoroughly. The substance of interest (e.g., the gas ofinterest) is then injected into the test vessel using a syringe pumpuntil a specified initial pressure is reached. The reference vessel isblank. The test system is placed at a temperature such that thesubstance of interest is in the liquid phase and maintained at thattemperature. With a heating rate of about 0.03° C./min, the systemtemperature is then increased while the heat flow and pressure historyare continuously recorded until an exothermic peak appears in thethermogram, after which the system temperature is restored to ambientconditions. The procedure is repeated for different initial pressures.

D. Measuring the Onset of the Vapor-Liquid Phase Transition inNanopores—Isochoric Evaporation-Point Measurement

The capillary evaporation of CO₂ and ethane in SBA-15 mesoporous silicawith different pore diameters (adsorbent S2 and adsorbent S3) weremeasured using the isochoric evaporation-point procedure provided above.The only difference is that for tests containing adsorbent, a certainamount of SBA-15 is first introduced into the test vessel using a smallspatula. Such amounts of SBA-15 are provided above. The adsorbent iskept in a drying oven at about 120° C. for about 24 hours prior to thetest.

The isochoric methods described herein accurately determine the onsetconditions for vapor-liquid phase transitions for substances andmixtures of substances in bulk and in pores, e.g., nanopores. Theisochoric methods and systems described herein rival and/or surpassconventional methods for measuring vapor pressures, dew points,capillary condensation, and capillary evaporation of substances. Forexample, unlike the conventional isobaric methods, there is no need tooptimize the sample size, pinhole size, and the scanning rate of thesample in order to obtain accurate results. Moreover, the isochoricmethods and systems described herein are applicable to, at least,volatile substances, high pressure systems, capillary condensation, andcapillary evaporation measurements. Further, the isochoric methodsdescribed herein are much less time consuming than typical adsorptionexperiments, reducing the time utilized for measuring a capillarycondensation point (or capillary evaporation point) from days, or evenweeks, to a few hours.

All documents described herein are incorporated by reference herein,including any priority documents and/or testing procedures to the extentthey are not inconsistent with this text. As is apparent from theforegoing general description and the specific embodiments, while formsof the present disclosure have been illustrated and described, variousmodifications can be made without departing from the spirit and scope ofthe present disclosure. Accordingly, it is not intended that the presentdisclosure be limited thereby. Likewise, the term “comprising” isconsidered synonymous with the term “including.” Likewise whenever acomposition, an element or a group of elements is preceded with thetransitional phrase “comprising,” it is understood that we alsocontemplate the same composition or group of elements with transitionalphrases “consisting essentially of,” “consisting of,” “selected from thegroup of consisting of,” or “is” preceding the recitation of thecomposition, element, or elements and vice versa.

For the sake of brevity, only certain ranges are explicitly disclosedherein. However, ranges from any lower limit may be combined with anyupper limit to recite a range not explicitly recited, as well as, rangesfrom any lower limit may be combined with any other lower limit torecite a range not explicitly recited, in the same way, ranges from anyupper limit may be combined with any other upper limit to recite a rangenot explicitly recited. Additionally, within a range includes everypoint or individual value between its end points even though notexplicitly recited. Thus, every point or individual value may serve asits own lower or upper limit combined with any other point or individualvalue or any other lower or upper limit, to recite a range notexplicitly recited.

What is claimed is:
 1. A process for measuring a vapor-liquid transitionof a substance in a constant volume system, comprising: (a) introducinga substance into a sample cell of a calorimetric block of a differentialscanning calorimeter (DSC) at a first initial pressure, the systemvolume being constant; (b) maintaining the substance in a vapor phase;(c) cooling the substance at a cooling rate; and (d) generating athermogram.
 2. The process of claim 1, further comprising furthercomprising evacuating the system prior to introducing the substance intothe sample cell.
 3. The process of claim 1, further comprising:performing operation (a) at a second initial pressure, the secondinitial pressure being different from the first initial pressure; andperforming operations (b), (c), and (d).
 4. The process of claim 1,wherein the substance comprises more than one compound.
 5. The processof claim 1, wherein the cooling rate is from about 0.01° C./min to about0.1° C./min.
 6. The process of claim 1, wherein the cooling rate isabout 0.03° C./min.
 7. The process of claim 1, wherein the substancecomprises a hydrocarbon, a substituted hydrocarbon, or a combinationthereof.
 8. The process of claim 1, wherein the substance comprises CO,CO₂, N₂, SO₂, Ar, or a combination thereof.
 9. A process for measuring avapor-liquid transition of a substance in a constant volume system,comprising: (a) introducing a substance into a sample cell of acalorimetric block of a differential scanning calorimeter (DSC) at afirst initial pressure, the system volume being constant; (b)maintaining the substance in a liquid phase; (c) heating the substanceat a heating rate; and (d) generating a thermogram.
 10. The process ofclaim 9, further comprising evacuating the system prior to introducingthe substance into the sample cell.
 11. The process of claim 9, furthercomprising: performing operation (a) at a second initial pressure, thesecond initial pressure being different from the first initial pressure;and performing operations (b), (c), and (d).
 12. The process of claim 9,wherein the substance comprises more than one compound.
 13. The processof claim 9, wherein the heating rate is from about 0.01° C./min to about0.1° C./min.
 14. The process of claim 9, wherein the heating rate isabout 0.03° C./min.
 15. The process of claim 9, wherein the substancecomprises a hydrocarbon, a substituted hydrocarbon, or a combinationthereof.
 16. The process of claim 9, wherein the substance comprises CO,CO₂, N₂, SO₂, Ar, or a combination thereof.
 17. A process for measuringa vapor-liquid transition of a substance in a constant volume system,comprising: (a) introducing an adsorbent into a sample cell of acalorimetric block of a differential scanning calorimeter, the systemvolume being constant; (b) introducing a substance into the sample cellat a first initial pressure; (c) maintaining the substance in a vaporphase or maintaining the substance in a liquid phase; (d) cooling thesubstance at a cooling rate when the process comprises maintaining thesubstance in a vapor phase, or heating the substance at a heating ratewhen the process comprises maintaining the substance in a liquid phase;and (e) generating a thermogram.
 18. The process of claim 17, whereinthe adsorbent comprises a microporous particle, a nanoporous particle, amesoporous particle, or a combination thereof.
 19. The process of claim17, further comprising evacuating the system prior to introducing thesubstance into the sample cell.
 20. The process of claim 17, furthercomprising performing operations (a)-(e), wherein operation (b) isperformed at a second initial pressure, the second initial pressurebeing different from the first initial pressure.